A higher dimensional stationary rotating black hole must be axisymmetric

DOI10.1007/s00220-007-0216-4zbMath1128.83028arXivgr-qc/0605106OpenAlexW2022227375WikidataQ125975074 ScholiaQ125975074MaRDI QIDQ2385029

Stefan Hollands, Robert M. Wald, Akihiro Ishibashi

Publication date: 11 October 2007

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/gr-qc/0605106

Mathematics Subject Classification ID

Black holes (83C57) Applications of global differential geometry to the sciences (53C80) Kaluza-Klein and other higher-dimensional theories (83E15)

Related Items (74)

Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS ⋮ Mathematical general relativity: A sampler ⋮ Symmetry enhancement of extremal horizons in D   =  5 supergravity ⋮ Black rings at large \(D\) ⋮ New geometries for black hole horizons ⋮ Black holes with a single Killing vector field: black resonators ⋮ Stability of black holes and black branes ⋮ Black holes and Black strings in plane waves ⋮ Essentials of blackfold dynamics ⋮ New horizons for black holes and branes ⋮ Scaling and universality in extremal black hole perturbations ⋮ Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface ⋮ Einstein-Gauss-Bonnet black rings at large \(D\) ⋮ Symmetries of vacuum spacetimes with a compact Cauchy horizon of constant nonzero surface gravity ⋮ On the existence of stationary Ricci solitons ⋮ Topology of supersymmetric \(\mathcal{N} = 1\), D = 4 supergravity horizons ⋮ New generalized nonspherical black hole solutions ⋮ Superradiance and black resonator strings encounter helical black strings ⋮ Towards fluid instabilities of stationary non-Killing horizons ⋮ Gluing variations ⋮ Generalizations and challenges for the spacetime block-diagonalization ⋮ Analyticity of quasinormal modes in the Kerr and Kerr-De Sitter spacetimes ⋮ A stationary black hole must be axisymmetric in effective field theory ⋮ A uniqueness theorem for stationary Kaluza-Klein black holes ⋮ Kerr black string flow ⋮ Non-singular spacetimes with a negative cosmological constant: IV. Stationary black hole solutions with matter fields ⋮ Supersymmetric black holes with a single axial symmetry in five dimensions ⋮ Near-horizon geometries of supersymmetric \(AdS_{5}\) black holes ⋮ Moduli space of supersymmetric solitons and black holes in five dimensions ⋮ Black holes with only one Killing field ⋮ Ultraspinning instability: the missing link ⋮ Bounding horizon area by angular momentum, charge, and cosmological constant in 5-dimensional minimal supergravity ⋮ An instability of higher-dimensional rotating black holes ⋮ Extension of Killing vector fields beyond compact Cauchy horizons ⋮ New restrictions on the topology of extreme black holes ⋮ Travel time tomography in stationary spacetimes ⋮ Instabilities of extremal rotating black holes in higher dimensions ⋮ First law of black hole in the gravitational electromagnetic system ⋮ On higher dimensional black holes with Abelian isometry group ⋮ Multiple Killing horizons: the initial value formulation for Λ -vacuum ⋮ Thermodynamic instability of doubly spinning black objects ⋮ Holographic insights and puzzles ⋮ Uniqueness theorem for 5-dimensional black holes with two axial Killing fields ⋮ Uniqueness of supersymmetric AdS₅ black holes with SU(2) symmetry ⋮ Black holes in higher dimensions ⋮ Three-dimensional black holes and descendants ⋮ Stationary black holes and attractor mechanism ⋮ Further restrictions on the topology of stationary black holes in five dimensions ⋮ An infinite class of extremal horizons in higher dimensions ⋮ HIGHER DIMENSIONAL BLACK HOLES ⋮ Black hole thermodynamics: general relativity and beyond ⋮ Heterotic black horizons ⋮ Higher-dimensional rotating charged black holes ⋮ Existence and uniqueness of near-horizon geometries for 5-dimensional black holes ⋮ A Bakry-Émery almost splitting result with applications to the topology of black holes ⋮ Asymptotic flatness at spatial infinity in higher dimensions ⋮ A classification of near-horizon geometries of extremal vacuum black holes ⋮ Black string flow ⋮ Symmetries of cosmological Cauchy horizons with non-closed orbits ⋮ Black resonators and geons in AdS ₅ ⋮ Black Holes in Higher-Dimensional Gravity ⋮ Abbott–Deser–Tekin like conserved quantities in Lanczos–Lovelock gravity: beyond Killing diffeomorphisms ⋮ Exact black-hole formation with a conformally coupled scalar field in three dimensions ⋮ The Kerr/CFT correspondence and its extensions ⋮ Plumbing constructions and the domain of outer communication for 5-dimensional stationary black holes ⋮ Steady states of holographic interfaces ⋮ To go or not to go with the flow: Hawking radiation at strong coupling ⋮ On the `Stationary implies axisymmetric' theorem for extremal black holes in higher dimensions ⋮ Black hole topology in ${f(R)}$ gravity ⋮ Multiple Killing horizons ⋮ The Kerr/CFT correspondence and its extensions ⋮ Stationary black holes: uniqueness and beyond ⋮ Classification of near-horizon geometries of extremal black holes ⋮ Wave equations with initial data on compact Cauchy horizons

Cites Work

• Unnamed Item
• Unnamed Item
• On local and global existence of Killing vector-fields
• Symmetries of cosmological Cauchy horizons
• Black holes in higher dimensional space-times
• On the global existence and the asymptotic behavior of solutions to the Einstein-Maxwell-Yang-Mills equations
• Maximal hypersurfaces in stationary asymptotically flat spacetimes
• On rigidity of analytic black holes
• On the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon
• Uniqueness and Nonuniqueness of Static Black Holes in Higher Dimensions
• Uniqueness theorem for static black hole solutions of  -models in higher dimensions
• Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations
• Proof of uniqueness of the Kerr-Newman black hole solution
• Symmetries of cosmological Cauchy horizons with exceptional orbits
• Extensions of spacetimes with Killing horizons
• On spacetimes containing Killing vector fields with non-closed orbits
• Axisymmetric metrics in arbitrary dimensions
• Global extensions of spacetimes describing asymptotic final states of black holes
• On further generalization of the rigidity theorem for spacetimes with a stationary event horizon or a compact Cauchy horizon
• The Large Scale Structure of Space-Time
• The AdS/CFT correspondence and topological censorship

This page was built for publication: A higher dimensional stationary rotating black hole must be axisymmetric